Question

Solve the differential equation:

Answer 1

I solved the Characteristic equation and got:

Answer 2

that could be either laplace transform problem or a constant coefficent problem

Answer 3

y(t)=C1e^(-t)+C2r^(-t)

Answer 4

But that's wrong.

Answer 5

Not Laplace. We're not that far yet.

Answer 6

wait waIT WAIT. SORRY CAPS. I'll solve it both ways and upload k?

Answer 7

Okay,

Answer 8

Just explain me this.

Answer 9

Wolfream says y(t)= C1e^(-t) + C2 te^(-t) is the solution.

Answer 10

Where did they get the second t from in the second term?

Answer 11

we have 2 same root

Answer 12

I know that. Why do they have that extra t though?

Answer 13

yeah it's a repeating root so you have to add the extra x or t in this case

Answer 14

Why so? That's what's confusing me :P .

Answer 15

because ok we factor first and got noooooooo we change it into r^2+2r+1 = 0 and that factors nicely to (r+1)(r+1) = 0 since r = -1 and it's repeating twice we have to write c1e^-x + c2e^-x (x) = y

Answer 16

But why? >.< .

Answer 17

It makes sense otherwise and I can solve the rest on my own :P .

Answer 18

because r = -1 not once but twice...

Answer 19

I'm in a differential equations course and I can't remember my basic algebra >.< .

Answer 20

you have (r+1)(r+1) = 0
r = -1 not once but twice... that's a repeated root
should you have r = 2 r = 4 that's a real root and thus you have to write c1e^2x + c2e^4x = y . I just took this course last semester

Answer 21

Ahh I see. I'm going ahead of myself because i'm not at repeated roots yet :P . I'm getting ahead of myself. Thanks!

Answer 22

How was Calc iv btw? :P .

Answer 23

there's a third one... complex root which takes the form of e^(ALPHA)x[cos(BETAX)c1+sin(BETA)c2]
I passed it but then again my prof sucked... if it wasn't for the curve, he would've easily failed the class D:

Answer 24

Haha I liked Calc iv XD . This differentials equations course will be killer though :( .

Answer 25

oops erase the X in beta X
where alpha +/-beta (i)
i = imaginary

Answer 26

actually it's easier than calc iv XD

Answer 27

Yep I knew what you meant :P .

Answer 28

REALLY?!?! That's a first :P .

Answer 29

how the heck did I get an A - in differential equations and a C in calc 4?

Answer 30

THen this course should be a piece of cake.

Answer 31

I for an A in Calc iv .

Answer 32

So... But i'm not sure :( .

Answer 33

easier than what I'm doing now.

Answer 34

got*

Answer 35

Well hat's good to know :) .

Answer 36

http://openstudy.com/study#/updates/52db5f51e4b05a53debcfc5a

Answer 37

Eww...

Answer 38

yeahhhhh that ********** is required for all math majors.

Answer 39

this one problem is killing me. I got 1.4.16 with ease

Answer 40

I'm doing math after Engineering >.< .

Answer 41

math is computation and proof. computation is awesome proof can go to the pits